End behavior of $$$f{\left(x \right)} = - 3 x^{4} + 2 x^{3} - x^{2} + 4$$$

Find the end behavior of $$$f{\left(x \right)} = - 3 x^{4} + 2 x^{3} - x^{2} + 4$$$.

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is $$$- 3 x^{4}$$$, the degree is $$$4$$$, i.e. even, and the leading coefficient is $$$-3$$$, i.e. negative.

This means that $$$f{\left(x \right)} \rightarrow -\infty$$$ as $$$x \rightarrow -\infty$$$, $$$f{\left(x \right)} \rightarrow -\infty$$$ as $$$x \rightarrow \infty$$$.

For the graph, see the graphing calculator.

$$$f{\left(x \right)} \rightarrow -\infty$$$ as $$$x \rightarrow -\infty$$$, $$$f{\left(x \right)} \rightarrow -\infty$$$ as $$$x \rightarrow \infty$$$.